Flow measurement devices having constant relative geometries

ABSTRACT

Systems and methods are disclosed for differential pressure meters having a constant beta edge boundary defined by fluid displacement members of the meter. In some embodiments, a differential pressure meter may have an interchangeable fluid displacement member, such that each fluid displacement member replaced in the meter maintains a constant beta edge boundary. In other embodiments, a family of differential pressure meters having permanent fluid displacement members may maintain a constant beta edge boundary for each meter of the family of differential pressure meters.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.13/007,560, entitled “FLOW MEASUREMENT DEVICES HAVING CONSTANT RELATIVEGEOMETRIES”, filed Jan. 14, 2011, which is herein incorporated byreference in its entirety.

BACKGROUND

This section is intended to introduce the reader to various aspects ofart that may be related to various aspects of the present invention,which are described and/or claimed below. This discussion is believed tobe helpful in providing the reader with background information tofacilitate a better understanding of the various aspects of the presentinvention. Accordingly, it should be understood that these statementsare to be read in this light, and not as admissions of prior art.

Transport of fluids, such as in oil and gas systems, power generationsystems, etc., relies on a variety of components and devices. Forexample, fluids may be transported through a complex network of pipes,fittings, and processing equipment. Such networks may be a part ofpipelines or other transportation structures to transport the fluid froma source to a destination, such as further transportation systems orstorage facilities. Such pipelines or other transportation structuresmay include pressure control, regulation, and safety devices, which mayinclude valves, actuators, sensors, and electronic circuitry.

It may be desirable to measure the flow rate of the fluid in suchsystems. One particular type of flow rate measurement device may bereferred to as a differential pressure meter. A differential pressuremeter places a fluid displacement member centrally within the flow pathof a fluid. As the fluid flows around the displacement member, the fluiddisplacement member causes differential pressure in the fluid. Thedifference in pressure may be measured via taps disposed on the upstreamand downstream portions of the fluid displacement member. The flow rateof the fluid may be determined from the difference in pressure.

The differential pressure meters are designed for use with andcalibrated for specific types of fluids and flow rate ranges. Duringoperation, the actual flow rate of a fluid may be outside the rangemeasured by the meter, and, the type or composition of the fluid mayalso change.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features, aspects, and advantages of the present invention willbecome better understood when the following detailed description is readwith reference to the accompanying figures in which like charactersrepresent like parts throughout the figures, wherein:

FIG. 1 is a diagram of a differential pressure flow meter in accordancewith an embodiment of the present invention;

FIG. 2 is a partial cross-section of the meter of FIG. 1 in accordancewith an embodiment of the present invention;

FIGS. 3A-3C are partial cross-sections of a differential flow meterhaving an interchangeable fluid displacement member that maintains aconstant beta edge boundary in accordance with an embodiment of thepresent invention;

FIGS. 4A-4C are graphs plotting the C.d. for differential pressuremeters each having a different beta ratio and maintaining a constantbeta edge boundary in accordance with an embodiment of the presentinvention;

FIG. 5 is an exploded view of a detachable fluid displacement member inaccordance with an embodiment of the present invention;

FIGS. 6A-6B are partial cross-sections of a family of differentialpressure meters having different fluid displacement members thatmaintain a constant beta edge boundary in accordance with an embodimentof the present invention;

FIGS. 7A-7B are partial cross-sections of a family of differentialpressure meters having different fluid displacement members thatmaintain a constant beta edge boundary in accordance with anotherembodiment of the present invention;

FIG. 8 is a flowchart of a process for operation of a differentialpressure meter in accordance with an embodiment of the presentinvention;

FIGS. 9A and 9B are partial cross-sections of a flangless differentialflow meter having an interchangeable fluid displacement member inaccordance with an embodiment of the present invention; and

FIG. 10 is an exploded perspective view of the flangless differentialpressure meter and interchangeable fluid displacement member of FIG. 9Ain accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

One or more specific embodiments of the present invention will bedescribed below. These described embodiments are only exemplary of thepresent invention. Additionally, in an effort to provide a concisedescription of these exemplary embodiments, all features of an actualimplementation may not be described in the specification. It should beappreciated that in the development of any such actual implementation,as in any engineering or design project, numerousimplementation-specific decisions must be made to achieve thedevelopers' specific goals, such as compliance with system-related andbusiness-related constraints, which may vary from one implementation toanother. Moreover, it should be appreciated that such a developmenteffort might be complex and time consuming, but would nevertheless be aroutine undertaking of design, fabrication, and manufacture for those ofordinary skill having the benefit of this disclosure.

Embodiments of the present invention include maintaining a constant betaedge boundary for a fluid displacement member of one or moredifferential pressure flow meters. In one embodiment, a differentialpressure meter may include an interchangeable fluid displacement memberthat maintains a constant distance between the beta edge boundary andthe center lines of the taps in the meter. In other embodiments, afamily of differential pressure meters may include different beta ratiofluid displacement members that maintain a constant distance between thebeta edge boundary and the center lines of the taps of each meter.

FIG. 1 depicts a system 10 having a flow measurement device, e.g., adifferential pressure flow meter 12, in accordance with an embodiment ofthe present invention. The differential pressure meter 12 includes ameter body 14 having a conduit 16 through which fluid may flow. A fluiddisplacement member 18 may be centrally disposed in the conduit 16 andsuspended from the conduit 16 via a support 19. Fluid may flow throughthe conduit 16 and over the fluid displacement member 18 in thedirection indicated by arrows 20. The fluid may flow into the conduit 16of the meter 12 either directly or indirectly from a source 24. Forexample, the source 22 may be a source of oil, natural gas (such as coalbed methane), steam, or any other suitable fluid. The meter body 14 mayinclude flanges 26 to provide for installation in a pipeline (e.g.,between pipe sections) or other transportation structure. The flanges 26may be secured to other structure via bolts, welds or any other suitabletechniques.

As the fluid flows through the conduit 16, the fluid displacement causedby the fluid displacement member 18 may introduce a difference inpressure between the upstream fluid (e.g., upstream of the member 18)and the downstream member (e.g., downstream of the member 18). In someembodiments, the fluid displacement member 18 may have one or morefrustum portions, conical portions, or any other shaped portionssuitable for creating a pressure differential in the fluid. In yet otherembodiments, multiple fluid displacement members may be included in themeter body 14 of the flow measurement device 12. In some embodiments,the fluid displacement member 18 may be removably attached by and to thesupport 19 such that the member 18 may be removed and/or replaced. Inother embodiments, the member 18 may be permanently secured by thesupport 19, such as by welding.

The meter body 14 may include an upstream pressure tap 28 in fluidcommunication with the conduit 16 and a downstream pressure tap 30 influid communication with the interior of the fluid displacement member18 and the downstream portion of the conduit 16, such as via hollowregion 32 (e.g., interior passage) of the support 19 and hollow region31 (e.g., interior passage) of the fluid displacement member 18. Thedifference in pressure measured at the upstream tap 28 and thedownstream tap 30 may be used to determine the flow rate of the fluidflowing through the conduit 16.

The upstream tap 28 and downstream tap 30 may be coupled to a valvemanifold 34. Valves 35 may be coupled between the manifold 34 and thetaps 28 and 30. The manifold 34 may be coupled to a transmitter 36 thatrecords the differential pressure signal generated by the meter 12 andprovides an output (e.g., an analog or serial output) to a computer 38,such as a flow computer or data control system having memory 39 andprocessor 40. The manifold 34 isolates the transmitter 36 from theprocess fluid and may enable maintenance and calibration of thetransmitter 36. It should be appreciated that the system 10 may includeany other devices suitable for controlling and/or monitoring the fluidflowing through the conduit 16, such as a resistance temperaturedetector (RTD).

FIG. 2 depicts a cross-section of the meter 12 illustrating the fluiddisplacement member 18 having an upstream frustum 42 and a downstreamfrustum 44 in accordance with an embodiment of the present invention. Asillustrated, the upstream frustum 42 comprises a diverging cone relativeto the fluid flow direction 20, whereas the downstream frustum 44comprises a converging cone relative to the fluid flow direction 20. Theinterface between the upstream frustum 42 and downstream frustum 44forms a peripheral edge 45 (also referred to as cantilevered edge). Theperipheral edge 45 forms a beta-edge boundary (also referred to as a“BEB”) 46 of the meter 12.

As shown in FIG. 2, the downstream frustum 44 may include a hole 47connected to hollow region 32 to enable fluid communication between thedownstream tap 30 and the fluid downstream from the member 18. The shapeof the member 18 may be designed to reshape the fluid velocity provideupstream of the member 18, creating a pressure drop between thedownstream and upstream portions of the fluid in the conduit 16.

The calibration and accuracy of the meter 12 depends in part on the“beta ratio” (also referred to as area ratio). The beta ratio refers tothe ratio between the diameter (“d”) of the peripheral edge 45 and thediameter (“D”) of the conduit 16. Additionally, the slope of thedownstream frustum 44 may be referred to as a “beta angle.” The betaratio may be determined as follows:

$\begin{matrix}{\beta = \frac{\sqrt{D^{2} - d^{2}}}{D}} & (1)\end{matrix}$

Where:

β=the beta ratio;D=the diameter of the conduit 16; andd=the diameter of the downstream frustum at the peripheral edge, i.e.,at the beta edge boundary.

Thus, for a given beta ratio, the diameter d of the peripheral edge 45may be determined as follows:

After determination of the Beta ratio, the mass flow rate of the fluidmay be determined as follows:

qm=N ₁ CdEvY(βD)²√{square root over (ρ_(t,p) ΔP)}  (2)

Where:

qm is the mass flow rate;N₁ is a units constant;Cd is a discharge coefficient that may determined during calibration ofthe meter;p_(t,p) is the fluid density at flowing conditions;ΔP is the differential pressure (that may be determined from datareceived the upstream tap 28 and downstream tap 30;

For Equation 2, Y may have a value of 1 for incompressible fluids. Forcompressible fluids, Y may be experimentally determined or calculated byvarious techniques, such as according to the following equation:

$\begin{matrix}{Y = {1 - {\left( {0.41 + {0.35\; \beta^{4}}} \right)\frac{\Delta \; P}{k}}}} & (3)\end{matrix}$

Where:

k is the gas isentropic exponent.

For Equation 2, Ev may be determined from the beta ratio (β) as follows:

$\begin{matrix}{{Ev} = \frac{1}{\sqrt{1 - \beta^{4}}}} & (4)\end{matrix}$

After determination of the mass flow rate, volumetric rates of the fluidmay be determined. For example, the volumetric flow rate at flowingconditions (also referred to as “gross” or “actual” flow rates) may bedetermined as follows:

$\begin{matrix}{{qv} = \frac{qm}{\rho_{t,p}}} & (5)\end{matrix}$

Where:

qv is the volumetric flow rate at flowing conditions.

Similarly, the volumetric flow rate at based conditions (also referredto as “standard” flow rates) may be determined as follows:

$\begin{matrix}{{Qv} = \frac{qm}{\rho_{b}}} & (6)\end{matrix}$

Where:

Qv is the volumetric flow rate at base conditions; andp_(b) is the fluid density at base conditions.

It should be appreciated that changes in temperature, Reynolds number ofthe fluid, or any other parameter may be compensated for in the aboveequations by using suitable correction techniques.

As described above, the beta ratio determined in Equation 1, and used inthe determination of mass flow rate in Equation 2, may be a function ofthe position of the beta edge boundary 46. Additionally, the calibrationinformation for the meter, such as the coefficient of discharge (C.d.)in Equation 2, may be a function of the position of the beta edgeboundary 46. The position of the beta edge boundary 46 may be definedrelative to the center line 48 of the upstream tap 28 and the centerline 50 of the downstream tap 30. Thus, the meter 12 may define adistance 52 between the beta edge boundary 46 and the center line 50 anda distance 54 between the beta edge boundary 46 and the center line 48of the upstream tap 28.

The fluid flowing from the source 24, such as a well, may be producedunder gradually less pressure as the amount of fluid in the welldecreases. In such an embodiment, the originally designed and calibratedbeta ratio of the meter 12 may have a measurable range unsuitable forthe lower flow rate of the fluid. Additionally, the meter 12 may bemoved and used in a new system having a different fluid flow rate or adifferent type of fluid. Typically, the beta ratio of the meter 12 maybe changed by shortening the length of the member 18, thus changing thediameter d of the peripheral edge 45. However, such changes in the betaratio also result in changing the coefficient of discharge (C.d.) forthe meter 12, thus changing the calibration parameters of the meter 12.As a consequence, by changing the member 18 in this manner, suchconventional meters also change the beta edge boundary, reducing orlengthening the beta edge boundary relative to other components of themeter 12.

FIGS. 3A-3C depict a differential pressure meter 60 having a removablefluid displacement member 62 that maintains a constant position of abeta edge boundary 64 in accordance with an embodiment of the presentinvention. The differential pressure meter 60 includes a meter body 66having a conduit 68 through which fluid may flow. The fluid displacementmember 62 may be centrally disposed in the conduit 68 and suspended fromthe conduit 68 via a support 70. The meter body 66 may include anupstream pressure tap 72 having a center line 74 and in fluidcommunication with the conduit 68 and a downstream pressure tap 76having a center line 78 in fluid communication with the interior of thefluid displacement member 62 and the downstream portion of the conduit68, such as via hollow region 80 (e.g., interior passage) of the support70 and hollow region 82 (e.g., interior passage) of the fluiddisplacement member 62.

The fluid displacement member 62 includes an upstream frustum 84 and adownstream frustum 86. As illustrated, the upstream frustum 84 comprisesa diverging cone relative to the fluid flow direction, whereas thedownstream frustum 86 comprises a converging cone relative to the fluidflow direction. As described above, the interface between the upstreamfrustum 84 and downstream frustum 86 forms a peripheral edge 88 thatdefines the beta edge boundary 64. The fluid displacement member 62 maydefine a beta ratio β₁ based on the diameter d₁ of the peripheral edge88 and the diameter D of the conduit 68.

The beta edge boundary 64 may be defined relative to the center line 74by a distance 92 and relative to the center line 78 by a distance 94.Additionally, the fluid displacement member 62 may be coupled to thesupport 80 by a barrel 96 having a length 100 and defined relative tothe center line 74 by a distance 102.

The fluid displacement member 62 may be interchangeable and may bedetached and replaced with an additional fluid displacement member 104,as shown in FIG. 3B, and an additional fluid displacement member 106, asshown in FIG. 3C. The fluid displacement member 62 may be coupled to thesupport 70 though any suitable attachment mechanism. For example, thestraight barrel 96 may include threads that couple to correspondingthreads on the support 70, as described below in FIG. 5. The fluiddisplacement member 62 may be secured by a central locking bolt 108inserted through the fluid displacement member 62.

As shown in FIG. 3B, the additional fluid displacement member 104 mayprovide a different beta ratio β₂, such as through a larger or smallerdiameter d₂ of a peripheral edge 112 of the member 104. The fluiddisplacement member 104 may include a barrel section 114 having a length116. Similarly, as shown in FIG. 3C, the additional fluid displacementmember 106 may provide a different beta ratio β₃, such as through asmaller diameter peripheral edge 119 of the member 106. The fluiddisplacement member 106 may include a barrel section 120 having a length122

As shown in FIGS. 3B and 3C, the additional fluid displacement members104 and 106 maintain a constant position of the beta edge boundary 64relative to the center line 74 and the center line 76. For example, asshown in FIG. 3B, the length 116 of the barrel section 114 may begreater than the length 100 of the barrel section 96 to maintain theposition of the beta edge boundary 64. In another example, as shown inFIG. 3C, the length 122 of the barrel section 120 of the fluiddisplacement member 106 may be greater than the length 100 to maintainthe position as the beta edge boundary 64. In other embodiments, thelength of a barrel section of a fluid displacement may be less than thelength 100 to maintain the position of the beta edge boundary 64.

Advantageously, the meter 60 depicted in FIGS. 3A, 3B, and 3C maymaintain a similar C.d. regardless of the use of fluid displacementmembers 62, 104, and 106. Thus, because the position of the beta edgeboundary 64 is maintained for each fluid displacement member, the meter60 may only require a single calibration and use of the same calibrationinformation, e.g., C.d., regardless of the beta ratio β₁, β₂, or β₃. Theelimination of additional calibration may increase the accuracy of themeter 60 across changes in fluid displacement members and beta ratios,while increasing ease of use and reducing maintenance.

FIGS. 4A-4C are graphs each depicting the C.d. for differentdifferential pressure meters each having a different beta ratio bututilizing the constant beta edge boundary technique described above. Thex-axis in each of FIGS. 4A-4C depicts the Reynolds number of waterflowing through one inch differential pressure meters and the y-axis ineach of FIGS. 4A-4C depicts the C.d. of the meter.

FIG. 4A depicts a first differential pressure meter having a beta ratioof 0.45. As shown in FIG. 4A, the C.d. of the meter is about 0.85throughout the illustrated range of Reynolds numbers. FIG. 4B depicts asecond differential pressure meter having a beta ratio of 0.65 andmaintaining the beta edge boundary in the same position as the metershown in FIG. 4A. As shown in FIG. 4B, the C.d. of the meter is about0.85 throughout the illustrated range of Reynolds numbers, about thesame C.d. as the meter shown in FIG. 4A. Finally, FIG. 4C depicts athird differential pressure meter having a beta ratio of 0.75 andmaintaining the beta edge boundary in the same position as the metershown in FIGS. 4A and 4B. As shown in FIG. 4C, the C.d. of the meter isabout 0.87 throughout the illustrated range of Reynolds numbers, aboutthe same C.d. as the meter shown in FIGS. 4A and 4B.

FIG. 5 is an exploded cross-sectional view of the fluid displacementmember 62 in accordance with an embodiment of the present invention. Asshown in FIG. 5, the fluid displacement member 62 further includes anextension 124, such as a cylinder adjacent to, or formed as an integralpart of, the upstream frustum 84. In one embodiment, particularlyapplicable when further stability is required (e.g., vibrating pipes andthe like), the fluid displacement member 62 also includes a contiguousbore 126 from the extension 124 to an attachment bore 128, which ishollowed out of the fluid displacement member 62. The bore 126 hasinternal threading 130 for screw threaded mating engagement withexternal threading 132 on the bolt 108. The attachment bore 128 hasinternal threading 134 for screw threaded mating engagement withexternal threading 136 on the barrel 96.

As also shown in FIG. 5, the support 70 includes a vertical bore 138 influid communication with the pressure tap 76 and the attachment bore140, oriented along the axial direction of the conduit 68, with internalthreading 142 for screw threaded mating engagement with externalthreading 144 on the barrel 96. The barrel 96 has external threading 144on one end, external threading 136 on another end, and at least one ofbores 146 drilled through the middle section of the barrel 96 such thatit is in fluid communication with adjacent fluid flow. The barrel 96also includes a longitudinal bore 148, which extends from the bores 146to the end of the component 96, and a hole 150, which is drilled throughexternal threading 144. The support 70 further mounts normally to thewall 32 of the conduit 68 by any means known in the art such that thevertical bore 138 aligns with the tap 76.

When assembled, external threading 144 of the barrel 96 is mated withinternal threading 142 of the attachment bore 140 of the support 70 suchthat the barrel 96 is inserted into and matingly engaged with theattachment bore 140 of the support 70. Upon such engagement, the hole150 should be aligned with the vertical bore 138 such that fluidcommunication is maintained between the tap 76, the vertical bore 138,the longitudinal bore 148, and at least one of the bores 146. Further,the fluid displacement member 62 is assembled with the bolt 108, theattachment bore 128 and the bore 126 as described above. Externalthreading 136 of the barrel 96 then is mated with internal threading 134on the attachment bore 128 such that the barrel 96 is inserted into andengaged with the attachment bore 128 and the fluid displacement member62.

As described above and shown in FIG. 5, the barrel 96 comprises at leastone bore 146 drilled through the barrel 96 such that the interior of thebarrel 96 is in fluid communication with fluid flow adjacent to thefluid displacement member 62. Preferably, a number of the bores 146 maybe provided through the barrel 96 so as to allow the tap 76 to sense thefluid pressure at in order to allow for the measurement of fluid flow.

Referring still to FIG. 5, the barrel 96 further includes an end portion152. In use, the end portion 152 may be matingly inserted intoattachment bore 128 to mount fluid displacement member 62 to support thebarrel 96 such that fluid displacement member 62 resides coaxiallywithin conduit 68. In this manner, fluid displacement member 62 isreadily attachable to and detachable from support 70 and interchangeablewith other fluid displacement members of different sizes and/ordifferent configurations to accommodate measurement of fluid flow withinthe conduit 62 of different fluids and different flow rates and tofacilitate use in the conduit 62 of fluid displacement members havingdifferent beta ratios, as described above in FIGS. 3B and 3C. As alsodescribed above, the bolt 108 with external threading 132 for screwthreaded mating engagement with internal threading 130 may be matinglyinserted into the fluid displacement member 62 and bore 126 by threadinginto the fluid displacement member 62 and bore 126, such that the bolt108 extends through the fluid displacement member 62, whereupon the bolt108 exits through attachment bore 128, and matingly inserts into areceiving slot 154 having internal threads 156.

External threading 136 on the end portion 152 and external threading 132on bolt 108 should cause rotation in opposite directions as the fluiddisplacement member 62 and the bolt 108, respectively, are installed.Thus, if either the member 62 or the bolt 108 rotates, the other tendsto resist such rotation providing for a more stable connection.Threading on either the end portion 152 or the bolt 108 can also be of adifferent type. For example, external threading 136 may be with coarsethreads while external threading 132 may be with fine threads. Tofurther secure the threads, a thread locking compound, such as Loctite®,could be applied to all threading. Moreover, as is well-known in theart, a screwdriver slot may be provided for tightening the fluiddisplacement member 62 and a hex socket may be provided for tighteningthe bolt 108.

The detachable mounting of fluid displacement member 62 to support 70 isadvantageous in terms of manufacture of fluid measurement systems.Standardized manufacturing procedures may be utilized to produce conduitsections of various standard diameters and fluid displacement members ofvarious standard diameters, configurations and beta ratios such thatfluid measurement systems meeting individual specifications can bequickly and economically assembled from standard, in-stock, commerciallyavailable components rather than being made to order. As describedabove, additional fluid displacement members 62 may be attached bybarrels 96 having different lengths to maintain the position of the betaedge ratio 64 with respect to the taps 72 and 76, e.g., to keep constantdistances 94 and 92.

In other embodiments, the beta edge boundary may be maintained in thesame position across a family of differential pressure meters having apermanent fluid displacement member disposed in the meter body. FIGS.6A-6C depict a differential pressure meter 150 having a permanentlycoupled fluid displacement member 152 having a beta edge boundary 154 inaccordance with an embodiment of the present invention. The differentialpressure meter 150 includes a meter body 156 having a conduit 158through which fluid may flow. The fluid displacement member 152 may becentrally disposed in the conduit 158 and suspended from the conduit 158via a support 160. The support 160 may be permanently coupled to thewall of the conduit 158, such as by welding, and the fluid displacementmember 152 may permanently coupled to the support 160, such as bywelding. In some embodiments, the fluid displacement member 152 andsupport 160 may be a single component. As also described above, themeter body 156 may include an upstream pressure tap 162 having a centerline 164 and in fluid communication with the conduit 158 and adownstream pressure tap 166 having a center line 168 in fluidcommunication with the interior of the fluid displacement member 152 andthe downstream portion of the conduit 158, such as via hollow region 170(e.g., interior passage) of the support 160 and hollow region 172 (e.g.,interior passage) of the fluid displacement member 152.

The fluid displacement member 172 may include an upstream frustum 174and a downstream frustum 176, similar to the embodiments describedabove. As described above, the interface between the upstream frustum174 and downstream frustum 176 forms a peripheral edge 178 that definesthe beta edge boundary 154. The fluid displacement member 172 may definea beta ratio β₁ based on the diameter d₁ of the peripheral edge 178 andthe diameter D of the conduit 158.

As described above, the beta edge boundary 154 may be defined relativeto the center line 164 by a distance 182 and relative to the center line168 by a distance 184. Additionally, the fluid displacement member 152may be coupled to the support 160 by a barrel 186 having a length 188and defined relative to the center line 164 by a distance 190.

As discussed above, by maintaining the position of the beta edgeboundary 154, the additional meter shown in FIG. 6B may have a similarC.d., and thus may use the same calibration information, as the meter150 depicted in FIG. 6A. For example, as shown in FIG. 6B, a secondmeter 192 may include a fluid displacement member 194 permanentlycoupled to a meter body 196 having a conduit 197 and having the samebeta edge boundary 154. The fluid displacement member 194 of the secondmeter 192 may be coupled to the meter body 196 by a support 198 and abarrel 200 in a manner similar to the meter 150. Additionally, the fluiddisplacement member 194 may also include an upstream frustum 202 and adownstream frustum 204 defining a peripheral edge 206 of the member 194at the beta edge boundary 154.

As shown in FIG. 6B, the meter 192 may have a different beta ratio β₂,based on the diameter D of the conduit 197 and the diameter d₂ of theperipheral edge 206. However, as also shown in FIG. 5B, the position ofthe beta edge boundary 154 is maintained relative to the center line 164of the tap 162 and the center line 168 of the downstream tap 166. Thus,the meter 192 may have the same C.d. as the meter 150, allowing themeter 192 to use the same calibration information as the meter 150. Insome embodiments, the beta edge boundary 154 may be maintained byincreasing a length 208 of the barrel 200, to compensate for a shorterupstream frustum 202, such that the length 208 is greater than thelength 188. Additionally, as shown in FIGS. 6A and 6B, the diameter D ofthe conduits 158 and 197 of each of the family of differential pressuremeters may be identical.

Additional differential pressure meters having permanently coupled fluiddisplacement members may use the techniques described above to maintaina beta edge boundary and enable reuse of calibration information acrossdifferent meters. For example, as noted in FIG. 6B, if the size of theupstream frustum is decreased, the length 208 of the barrel 200 may beincreased to maintain the position of the beta edge boundary 154relative to the center lines 164 and 168 of the taps 162 and 166respectively. Similarly, if the size of the upstream frustum isincreased, the length 208 of the barrel 200 may be decreased to maintainthe position of the beta edge boundary 154. Thus, all such meters in thefamily of differential pressure meters described above may have aconstant beta edge boundary.

In other embodiments, the beta edge boundary may be maintained in thesame position across a family of differential pressure meters withpermanent fluid displacement members disposed in a meter body havingwall taps, i.e., without a central tap. FIGS. 7A-7B depict a wall tapdifferential pressure meter 210 having a permanently coupled fluiddisplacement member 212 defining a beta edge boundary 214 in accordancewith an embodiment of the present invention. The differential pressuremeter 210 includes a meter body 216 having a conduit 218 through whichfluid may flow. The meter body 216 also includes an upstream wall tap220 having a center line 221 and a downstream wall tap 222 having acenter line 223 disposed in meter body 216 and in fluid communicationwith the conduit 218. The fluid displacement member 212 may be centrallydisposed in the conduit 218 and suspended from the conduit 218 via asupport 224. The support 224 may be permanently coupled to the wall ofthe conduit 218, such as by welding, and the fluid displacement member212 may be permanently coupled to the support 224, such as by welding.In some embodiments, the fluid displacement member 212 and support 224may be a single component.

As described above, in some embodiments the fluid displacement member212 may include an upstream frustum 226 and a downstream frustum 228that form a peripheral edge 230 that defines the beta edge boundary 214.The fluid displacement member 212 may define a beta ratio β₁ based onthe diameter d₁ of the peripheral edge 230 and the diameter D of theconduit 218.

As described above, the beta edge boundary 214 may be defined relativeto the center line 221 by a distance 234 and relative to the center line223 by a distance 236. Additionally, the fluid displacement member 212may be coupled to the support 224 by a barrel 238 having a length 240and defined relative to the center line 221 by a distance 242.

As discussed above, by maintaining the position of the beta edgeboundary 214, the additional meters, such as shown in FIG. 7B, may havea similar C.d., and thus may use the same calibration information, asthe meter 210 depicted in FIG. 7A. For example, as shown in FIG. 7B, asecond meter 244 may include a fluid displacement member 246 permanentlycoupled to a meter body 248 having a conduit 250 and having the sameposition of the beta edge boundary 214 relative to the wall taps 220 and222.

The fluid displacement member 246 of the second meter 244 may bepermanently coupled to the meter body 248 by a support 252 and a barrel254 having a length 255 in a manner similar to the meter 210.Additionally, the fluid displacement member 246 may also include anupstream frustum 256 and a downstream frustum 258 forming a peripheraledge 260 at the beta edge boundary 214.

As shown in FIG. 7B, the meter 244 may have a different beta ratio β₂,based on the diameter D of the conduit 250 and the diameter d₂ of theperipheral edge 260 of the member 246. However, as also shown in FIG.7B, the position of the beta edge boundary 214 is maintained relative tothe center line 221 of the tap 220 and the center line 223 of thedownstream tap 222. Thus, the meter 244 may have the same C.d. as themeter 210, allowing the meter 244 to use the same calibrationinformation as the meter 210. In some embodiments, the beta edgeboundary 214 may be maintained by increasing the length 255 of thebarrel 254, to adjust for a shorter upstream frustum 256, such that thelength 255 is greater than the length 240. In other embodiments, thebeta edge boundary 214 may be maintained by adjusting the position ofthe support 252 on the wall of the meter body 248, such as by moving thesupport 252 further downstream to maintain the position of the beta edgeboundary 214.

Additional differential pressure meters having permanently coupled fluiddisplacement members may use the techniques described above to maintaina beta edge boundary and enable reuse of calibration information acrossdifferent meters. For example, as noted in FIG. 7B, if the size of theupstream frustum is decreased, the length 255 of the barrel 254 may beincreased to maintain the position of the beta edge boundary 214relative to the center lines 221 and 223 of the wall taps 220 and 222respectively. Additionally, or alternatively, the position of thesupport 252 may be adjusted, such as by moving the support 252 furtherdownstream to maintain the position of the beta edge boundary 214.Similarly, if the size of the upstream frustum 256 is increased, thelength 255 of the barrel 254 may be decreased to maintain the positionof the beta edge boundary 214. Additionally, or alternatively, thesupport 252 may be moved further upstream to maintain the position ofthe beta edge boundary 214. Thus, all such meters in the family ofdifferential pressure meters described above may have a constant betaedge boundary.

FIG. 8 is a flowchart 270 depicting use of differential pressure metersaccording to the techniques described above. Initially, a beta edgeboundary for a differential pressure meter having a first beta ratio maybe determined (block 272), such as shown above in FIG. 2. The meter maybe calibrated based on the C.d. for that meter (block 274). In someembodiments, as shown above in FIGS. 3A-3C, the beta ratio of the metermay be changed by replacing the fluid displacement member of the meter(block 276). As also shown above in FIGS. 3A-3C, the replaced fluiddisplacement member may maintain the position of the beta edge boundaryof the meter (block 278). The meter may then be used with previouslydetermined calibration information (block 290).

In other embodiments, as shown above in FIGS. 6A-6B and FIGS. 7A-7B, thebeta ratio of may be changed by manufacturing and/or using another meterin a family of differential pressure meters, having, for example, apermanently coupled fluid displacement member (block 292). As also shownabove in FIGS. 6A-6B and FIGS. 7A-7B, the position of the beta edgeboundary may constant (block 294), such as by changing the length of thebarrel of a fluid displacement member or moving the support of a fluiddisplacement member. The new meter may then be used with previouslydetermined calibration information (block 290).

In other embodiments, the beta edge boundary may be maintained forinterchangeable fluid displacement members of other types ofdifferential pressure flow meters, such as a “flangless” differentialpressure meter. FIGS. 9A and 9B depict a flangless differential pressureflow meter 300 having removable fluid displacement members 302 and 304in accordance with an embodiment of the present invention. Thedifferential pressure meter 300 includes a flangless meter body 306having a conduit 308 through which fluid may flow. As shown in FIG. 9A,the fluid displacement member 300 may be centrally disposed in theconduit 308 and suspended from the conduit 308 via one or more supports310. The meter body 306 may include an upstream pressure tap 312 anddownstream pressure tap 314 in fluid communication with the conduit 308.

The fluid displacement member 302 may include an upstream frustum 316and a downstream frustum 318 that function in the manner described abovein FIGS. 3A-C. As described above, the interface between these frustums316 and 318 may form a peripheral edge 320 that defines a beta edgeboundary 322. The meter 300 and fluid displacement member 302 may definea beta ration B1 based on the diameter d1 of the peripheral edge 320 andthe diameter D of the conduit. As described above, the beta edgeboundary 322 may be defined relative to a center line 324 of theupstream tap and relative to a center line 326 of the downstream tap314.

The fluid displacement member 302 may be interchangeable and may bedetached from the supports 310 and replaced with the additional fluiddisplacement member 304, as shown in FIG. 9B, The fluid displacementmember 310 may be coupled to the supports 310, as shown below in FIG.10.

As shown in FIG. 9B, the additional fluid displacement member 304 mayprovide a different beta ratio β₂, such as through a larger or smallerdiameter d₂ of a peripheral edge 328 of the member 304. As shown inFIGS. 9A and 9B, the additional fluid displacement member 304 maintainsa constant position of the beta edge boundary 322 relative to the centerlines 324 and 326. For example, as shown in FIG. 9B, the length of asection 330 of the fluid displacement member 304 may be extended tomaintain the position of the beta edge boundary 322. In otherembodiments, the length of a barrel section of a fluid displacement maybe reduced to maintain the position of the beta edge boundary 322.

Advantageously, the meter 300 depicted in FIGS. 9A and 9B may maintain asimilar C.d. regardless of the use of fluid displacement members 302 and304, or other fluid displacement members that maintain the same betaedge boundary. Thus, the meter 300 may only require a single calibrationand use of the same calibration information, e.g., C.d., regardless ofthe beta ratio β₁, β₂, etc.

FIG. 10 is a perspective view of the flangless meter body 306 and thefluid displacement member 302 in accordance with an embodiment of thepresent invention. As shown in FIG. 10, the fluid displacement member302 may be coupled to an annular insert 334 having one or more of thesupports 310 extending radially from an inner wall of the insert 334.The supports 310 may be coupled to a receptacle 336 that receives thefluid displacement member 302. For example, the fluid displacementmember 302 may be coupled to the receptacle 336 via threads or any othersuitable coupling mechanism.

The annular insert 334 may be coupled to the meter body 306 viafasteners 338, e.g., bolts, screws, or other suitable fasteners. Thefasteners 338 may be inserted into holes 340 of the annular insert 334and into holes 342 of the meter body 306. The annular insert 334 may bereceived by a recess 344 of the meter body 306. In this manner, theannular insert 334 may provide for the removal and installation ofdifferent fluid displacement members that maintain the same beta edgeboundary, as described above. In some embodiments, the entire insert 334may be removed and replaced. In other embodiments, only the fluiddisplacement member 302 is removed from the meter 300 and replaced. Forexample, the fluid displacement member 302 may be removed from theinsert 334 and the fluid displacement member 304 may be installed in theinsert 334. Additionally, o-rings or other seals may be disposed oneither end of the meter body 306, such as on the insert 334.

While the invention may be susceptible to various modifications andalternative forms, specific embodiments have been shown by way ofexample in the drawings and have been described in detail herein.However, it should be understood that the invention is not intended tobe limited to the particular forms disclosed. Rather, the invention isto cover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the invention as defined by the followingappended claims.

1. A system, comprising: a plurality of interchangeable fluiddisplacement members, wherein each of the plurality of interchangeablefluid displacements members comprises a respective beta ratio, and aposition of a beta edge boundary for each of the plurality ofinterchangeable fluid displacement members is constant; and adifferential pressure meter that selectively uses one of the pluralityof interchangeable fluid displacement members.
 2. The system of claim 1,wherein each of the plurality of interchangeable fluid displacementmembers comprises a first frustum and a second frustum.
 3. The system ofclaim 2, wherein each of the plurality of interchangeable fluiddisplacement members comprise a peripheral edge at an interface betweenthe first frustum and the second frustum, wherein the peripheral edge isaligned with the beta edge boundary.
 4. The system of claim 1, whereinthe differential pressure meter comprises a first tap and second tap. 5.The system of claim 4, wherein the position of the beta edge boundary isconstant relative to the first tap or the second tap.
 6. The system ofclaim 4, wherein the first tap comprises a wall tap and the second tapcomprises a tap in fluid communication with an interior of one of theplurality of interchangeable fluid displacement members.
 7. The systemof claim 1, wherein the differential pressure meter comprises a support,wherein each of the plurality of interchangeable fluid displacementmembers is coupled to the differential pressure meter by the support. 8.The system of claim 7, wherein each of the plurality of interchangeablefluid displacement members is coupled to the support by a respectivebarrel.
 9. The system of claim 8, wherein the position of the beta edgeboundary is constant by changing a barrel of each of the plurality ofinterchangeable fluid displacement members, each barrel having adifferent length.
 10. The system of claim 7, wherein each of theplurality of interchangeable fluid displacement members is coupled tothe support via a threaded coupling and a bolt.
 11. A system,comprising: a family of differential pressure meters, wherein each meterof the family of differential pressure meters comprises a respective oneof a plurality of fluid displacement member permanently coupled to therespective meter, wherein the respective fluid displacement members haveidentical beta edge boundaries with respect to at least one tap of eachmeter of the family of differential pressure meters.
 12. The system ofclaim 11, wherein each of the plurality of fluid displacement members iswelded to a respective one of the family of differential pressuremeters.
 13. The system of claim 11, wherein each of the plurality offluid displacement members comprises a different beta edge ratio. 14.The system of claim 11, wherein the at least one tap comprises a walltap in a wall of a conduit of a respective one of the family ofdifferential pressure meters and a central tap in fluid communicationwith a respective one of the plurality of fluid displacement members.15. The system of claim 11, wherein the at least one tap comprises afirst wall tap in a wall of a conduit of a respective one of the familyof differential pressure meters and a second wall tap in fluidcommunication with a respective one of the plurality of fluiddisplacement members.
 16. The system of claim 11, wherein each of thefamily of differential pressure meters uses the same calibrationinformation, wherein the calibration information is based on theidentical beta edge boundaries.
 17. A kit, comprising: a plurality offluid displacement members, wherein each of the plurality of fluiddisplacements members comprises a respective beta ratio, and a positionof a beta edge boundary for each of the plurality of fluid displacementmembers is constant; a differential pressure meter that selectively usesone of the plurality of fluid displacement members; and instructions,comprising: instructions for calibrating the differential pressure meterhaving a first fluid displacement member and a first beta ratio toproduce a set of calibration data; instructions for installing a secondfluid displacement member having a second beta ratio; instructions foroperating the differential pressure meter having the second fluiddisplacement member using the set of calibration data determined withthe first fluid displacement member and the first beta ratio.
 18. Thekit of claim 17, wherein the instructions comprise instructions forremoving the first fluid displacement member via disengagement of one ormore threaded couplings.
 19. The kit of claim 17, wherein theinstructions comprise instructions for installing a third fluiddisplacement member having a third beta ratio.
 20. The kit of claim 19,wherein the instructions comprise instructions for operating thedifferential pressure meter having the third fluid displacement memberusing the set of calibration data determined with the first fluiddisplacement member and the first beta ratio